Functional Differential Operators and Equations |
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Author:
| Kurbatov, V. G. |
Series title: | Mathematics and Its Applications Ser. |
ISBN: | 978-0-7923-5624-0 |
Publication Date: | Apr 1999 |
Publisher: | Springer Netherlands
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Imprint: | Springer |
Book Format: | Hardback |
List Price: | USD $249.99 |
Book Description:
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This book deals with linear functional differential equations and operator theory methods for their investigation. The main topics are: the equivalence of the input-output stability of the equation
Lx = &mathsf; and the invertibility of the operator
L in the class of casual operators; the equivalence of input-output and exponential stability; the equivalence of the dichotomy of solutions for the homogeneous equation
Lx = 0 and the invertibility of the operator...
More DescriptionThis book deals with linear functional differential equations and operator theory methods for their investigation. The main topics are: the equivalence of the input-output stability of the equation Lx = &mathsf; and the invertibility of the operator L in the class of casual operators; the equivalence of input-output and exponential stability; the equivalence of the dichotomy of solutions for the homogeneous equation Lx = 0 and the invertibility of the operator L; the properties of Green's function; the independence of the stability of an equation from the norm on the space of solutions; shift invariant functional differential equations in Banach space; the possibility of the reduction of an equation of neutral type to an equation of retarded type; special full subalgebras of integral and difference operators, and operators with unbounded memory; and the analogue of Fredholm's alternative for operators with almost periodic coefficients where one-sided invertibility implies two-sided invertibility. Audience: This monograph will be of interest to students and researchers working in functional differential equations and operator theory and is recommended for graduate level courses.